This is the second companion paper of arXiv:1601.03586. We consider the morphism from the variety of triples introduced in arXiv:1601.03586 to the affine Grassmannian. The direct image of the dualizing complex is a ring object in the equivariant derived category on the affine Grassmannian (equivariant derived Satake category). We show that various constructions in arXiv:1601.03586 work for an arbitrary commutative ring object. The second purpose of this paper is to study Coulomb branches associated with star shaped quivers, which are expected to be conjectural Higgs branches of $3d$ Sicilian theories in type $A$ by arXiv:1007.0992.

中文翻译：

---

由库仑分支产生的等变派生 Satake 范畴中的环形物体

这是 arXiv:1601.03586 的第二篇配套论文。我们考虑从 arXiv:1601.03586 中引入的各种三元组到仿射 Grassmannian 的态射。二元复合体的直接图像是仿射格拉斯曼上的等变派生范畴（等变派生佐竹范畴）中的环对象。我们展示了 arXiv:1601.03586 中的各种构造适用于任意交换环对象。本文的第二个目的是研究与星形箭袋相关的库仑分支，这些分支预计是 arXiv:1007.0992 的 $A$ 类型的 $3d$ 西西里理论的推测希格斯分支。